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A337993 Numbers k such that L(k) < sigma(k) + k/Pi^2, where L(k) = floor(H(k) + exp(H(k)) * log(H(k))) and H(k) = Sum_{j=1..k} 1/j. 1
1, 2, 4, 6, 12, 24, 60, 120, 360, 2520, 5040 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Conjecture: This sequence is finite.
REFERENCES
S. Ramanujan, Highly composite numbers, Proc. Lond. Math. Soc. 14 (1915), 347-409; reprinted in Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962.
LINKS
J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, arXiv:math/0008177 [math.NT], 2000-2001; Am. Math. Monthly 109 (#6, 2002), 534-543.
S. Ramanujan, Highly Composite Numbers, Proc. London Math. Soc. 2, 14, 1915, page 15.
FORMULA
k is a term of this sequence <==> A057640(k) < A000203(k) + k/A002388.
MATHEMATICA
A337993Q[n_] := With[{h = HarmonicNumber[n]}, Floor[h + Exp[h]*Log[h]] < DivisorSigma[1, n] + n/Pi^2];
Select[Range[5040], A337993Q] (* Paolo Xausa, Feb 01 2024 *)
CROSSREFS
Sequence in context: A162936 A036484 A212654 * A093036 A340548 A087997
KEYWORD
nonn,more
AUTHOR
Peter Luschny, Oct 15 2020
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)